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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Procedure â€” To Evaluate the Sum or Difference of Functions

Step 1 Use x = a to find f(a) and g(a)

Step 2 Find f(a) + g(a) or f(a) - g(a).

Example 1

Given f(x) = x3 - 9 and g(x) = x2 + 18, find (f + g)(x) when x = -2.

That is, find (f + g)(-2).

Solution

 Step 1 Use x = -2 to find f(-2) and g(-2).Substitute -2 for x in f(x). Simplify. Subtract. So, f(-2) = -17. Substitute -2 for x in g(x). Simplify. Add. So, g(-2) = 22. f(-2)      g(-2) = (-2)3 - 9 = -8 - 9 = -17 = (-2)2 + 18 = 4 + 18 = 22 Step 2 Find f(-2) = g(-2). Add. f(-2) + g(-2) = -17 + 22= 5

So, (f + g)(-2) = 5.

Example 2

Given f(x) = x4 + 20 and g(x) = 5x2, find (f - g)(x) when x = 3.

That is, find (f - g)(3).

Solution

 Step 1 Use x = 3 to find f(3) and g(3).Substitute 3 for x in f(x). Simplify. So, f(3) = 101. Substitute 3 for x in g(x). Simplify. So, g(3) = 45. f(3)     g(3) = (3)4 + 20 = 101 = 5(3)2 = 45 Step 2 Find f(3) - g(3). Subtract. f(3) - g(3) = 101 - 45 = 56

So, (f - g)(3) = 56.